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Abstract

The present invention proposes a technique to improve PSF model estimation. The invention combines skew normal distribution technique and a technique to generate PSF kernels for PET scanner to improve characterization of a PET scanner and image reconstruction. Detector response function is modeled with a skew normal distribution by minimizing the sum of squared difference between data and estimated function.

Country

Undisclosed

Language

English (United States)

This text was extracted from a Microsoft Word document.

At least one non-text object (such as an image or picture) has been suppressed.

This is the abbreviated version, containing approximately
44% of the total text.

The present invention relates generally to positron
emission tomography (PET) and more particularly to a technique to model detector
response function.

In PET imaging, system resolution is degraded by several
factors, such as, size of detector crystal size and uncertainty about location
of scintillation in the detectors. In order to recover

system resolution, a point-spread-function (PSF) is
generally applied in image reconstruction to model detector response function.
A commonly used PSF is in a form of normal distribution whose standard
deviation describes magnitude of resolution degradation.

As the detector pair moves away from center of field
of view (FOV), the detector response function attains asymmetry due to circular
nature of scanner gantry. In a conventional technique the asymmetry is modeled
by joining two half normal distributions. The two half normal distributions include
two different standard deviations that describe detector response on left and
right side of line-of-response (LOR) connecting a detector pair.

However, there are several limitations to the two-half
normal distribution algorithm. For example, in order to estimate standard
deviations of the left and the right half normal distribution, the acquired
data requires division into two halves. One half is required for estimating
parameters in left normal distribution and the other half is required for estimating
parameters in right normal distribution. Asymmetry in the data generates
unequal number of data points in the left half and the right half of the data. Consequently,
unequal noise is generated in the estimated parameters for the two halves. For
the most asymmetrical case, narrower half may have very few data points for a
reliable estimation of standard deviation of the normal distribution. Further, division
of data into two halves requires estimation of maximum data point. This is due
to a possibility that actual maximum is not one of the data points. Figure 1
depicts data profile of a point source scan as a function of radial location
and illustrates that actual maximum may not be one of the data points.

Figure 1

In the example given in Figure 1 above, intensity
profile of a point source scan which is used to estimate the PSF is plotted as
a function of radial distance from center of the FOV. Due to close values of
the three highest data points it is difficult to determine the actual maximum. In
order to divide the data into two halves, the actual maximum requires to be
first estimated. As a result, uncertainty is created in the parameter estimation.
Also, the example given in Figure 1 depicts that the right half includes fewer
data points than the left half. Consequently, higher noise is created in the
estimated parameters.

It would be desirable to have an efficient technique to
improve PSF model estimation.